A black hole cast on a non-commutative background

TL;DR

This paper presents an exact solution for a black hole on a non-commutative background, revealing a non-singular, holographic, and quantized black hole model with fixed density and no mass-confinement degeneracy.

Contribution

It introduces a novel mechanism where matter density deforms into two distinct fields on a non-commutative background, leading to a non-singular, quantized black hole solution.

Findings

Black hole size is quantized as L=2N√θ.

The model is non-singular and holographic.

Energy-stress tensor satisfies classical energy conditions.

Abstract

In this work we describe a black hole, set on a non-commutative background. The model, which is relatively simple, is an exact solution of the Einstein Field Equations. Based on a proposition we put forward, we argue that introducing a matter density field on a non-commutative background sets up a mechanism that deforms the field into two distinct fields, one residing dominantly on the lattice tops (hereafter, on-cell) and the other residing dominantly in the inter-lattice regions (hereafter, off-cell). The two fields have different physical and themodynamic characterics which we describe, and some of which play a role in halting collpse to a singularity. For example, not surprisingly the on-cell (off-cell) fields manifest standard on-shell (off-shell) characteristics, respectively. Both the density and the net mass-energy are unchanged by the deformation mechanism. In our treatment the mass of a black hole defines its own size scale L of the interior region it occupies. Moreover, such a length is quantized, L=2N\sqrt{\theta}, in terms of a minimum length scale \sqrt{\theta}. The approach has the advantage that there is no degeneracy in mass-confinement since, here, the black hole density is not a function of the mass (as is the case in some recent treatments). The density is, instead a fixed quantity. As such, the approach puts an upper bound on black hole density, making it a universal parameter. The picture that emerges is that a black hole defined on a non-commutative background is both non-singular, holographic and quantized. Yet we also find, interestingly, that when taken over L the average value of the associated energy-stress tensor of the fields satisfies all classical energy conditions of GR.